This research paper is going to be over the physics of springs. I am going to be covering many points that are going to be covered. Some of these points include Hooke’s Law, simple harmonic motion, and many other topics.Some definitions suggest that a spring is an object that is used to store mechanical energy. Most springs are made up of some sort of metal, usually steel. When an external force is applied on a spring, it changes its shape while storing potential energy. When the external force stops acting on it, the spring will return to its original shape. If there is to much force applied to the spring, then the spring will deform and never return to it’s original shape. Springs are typically pushed, pulled, or pressed. There are many different types of springs. Most springs are made up of wire that has been wound multiple times into a circular shape. There are three basic types of wire springs. The first type of basic spring is the extension spring. The extension spring has tightly wound springs that are close together. When the spring is pulled on by an end and the other end is connected to something then it will pull back with the same amount of force to keep the object in it’s original place until the pull force exceeds the force it can pull back. The next type of basic spring is the compression spring. This spring is wound to have spaces in between the wire. This spring is designed to shorten. The way this spring is shortened is that when a force is applied to an end it will push back with the same force. If there is to much force applied then the spring will deform and may bend. The last type of basic spring is the torsion spring. This spring has two ends to it. there is just a few coils in between the two ends. When there is a force applied to both ends then the coils in the middle will tighten together. When the spring tightens it will pull it back to its original place. (see __http://school.mech.uwa.edu.au/~dwright/DANotes/springs/intro/intro.html__ also see __http://www.madehow.com/Volume-6/Springs.html__ ) Springs have been used through out history. Many things could have been used as spring type contraptions. The idea of a spring is to make the work easier of some task. The first type of springs that were used were non-coil type springs. A simple twig bending is an example of a type of spring force. The way people back in b.c. have thought of ways to improve springs. They constructed ways out of metals and wood. Ctesibius of Alexandria came up with a procedure of making "springy bronze" by increasing the proportion of tin in the copper alloy, casting the part, and hardening it with hammer blows.(quotation from __http://www.madehow.com/Volume-6/Springs.html__ ) Many other B.C. figures also contributed to make springs better. The uses for springs are endless. The main idea of a spring to do work is by how it can deform. After it deforms the spring should come back to its original shape and its position. Many other things were used in place of springs. For example clocks were controlled by a series of weights instead of a spring. The spring made the clock more accurate by being wound and back to its original position. The way springs came into society was by someone doing an ordinary job. The job for example was necessary to survive. Hunting was one of the main ways to survive. people were inefficient at killing their prey. To improve their hunting strategies they invented a bow and arrow. This spring like contraption probably kick started the need to learn more about how to improve this. It contributes to how we today got to such a complex design. There are many different types of designs. Different springs do different jobs. The basic design is to help how we live today. This is a major form of improved technology. The technology behind springs is endless. There are so many things to account for. A few things are the deforming point, how much stress the spring can take, and the elasticity. A guy named Robert Hooke discovered a way to measure elasticity. He called this Hooke’s law. In this law he described as an object deforms the force is greater. He also described the objects such as springs having a deforming limit beyond repair. He described this deformation as displacement of the molecules and ions in the material. The deforming of the spring can happen through many ways. Some ways of the springs that they can deform are by stretching, pulling, squeezing, compressing, bending, or twisting the spring. The springs have the ideal form of elasticity according to Robert Hooke. He stated that the F=kx or F=-kx, depending on the way you look at the constant. This basically states that when the force is applied then it is equal to the constant of the spring times the distance of deformation. He could calculate the spring constant by testing out springs. This helps us a lot today in our present times for simple task. Through just this simple equation we can find out how much load a spring can handle. The spring stores energy from when the force is applied. The more force you apply the more the distance it displaces from the original shape. This means that the force applied is directly proportional to the distance it displaces. Once the force is taken away the spring goes back to its original position. Force can also be expressed in terms of stress. Stress can be applied through work. (see __http://www.britannica.com/EBchecked/topic/271336/Hookes-law)__ Robert Hooke was a well known English scientist. He was born in Freshwater, Isle of Wight. He was almost as well known as Newton. Newton was one of his well known rival. He studied most of his life on how to make things better. He also discovered many things about microscopes. Today his teachings and discoveries help us through a lot. The springs in vehicles help ride smooth. we can only imagine what life would be without springs.(see __http://www.rod.beavon.clara.net/robert_hooke.htm__ and __http://www.roberthooke.com/)__ Springs can also be thought as of waves. When the spring does the same repetitive motion from one end to the back it is said to be in a state of oscillation. The oscillation happens when there is a simple harmonic motion. The motion is going in a repetitive like motion. Springs are technically designed to do this motion. The motion helps many other inventions do what they were designed for. The equilibrium of the spring is what causes this. As Robert Hooke came to find this fact out he also used his knowledge to calculate the equilibrium constant. He viewed these springs as ether stretched or compressed. He saw that it would go almost that same distance in the opposite direction. When the constant increases the more force it requires to make the same distance of displacement. (see __http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section4.rhtml)__ Gravity may some times affects the way springs work. It applies a downward force on the spring. By knowing this we also know that there is always constant force in the downward direction on the spring. Springs are designed to resist this given force. The only time that gravity can be ignored is when the weight on the spring passes through its equilibrium with maximum speed. Because gravity sometimes affects springs, we can use springs to understand gravity better. (see __http://www.newton.dep.anl.gov/askasci/phy00/phy00636.htm)__ Using springs as pendulums we can view how gravity shifts. Because this shift we can observe how the Earth moves by just looking at the springs. For a little time the spring pendulum will go in a straight path but it will slowly shift. The oscillations are what most physicist look at. They also look at what direction its going in. The spring may also have a little bounce in it. These effects are because of how the Earth moves. (see __http://www.astro.oma.be/ICET/bim/bim138/vanruymbeke2.htm)__ The quality of a spring depends on how high quality of the steel is. There are other factors like how tightly the spring was wound that would differ the quality. Also the quality of the spring depends on the thickness of the wire. A spring that has a high tendency of reaching it’s equilibrium faster is said to be a high quality spring. Depending on the job the spring has to do determines where the equilibrium on the spring is. For more powerful jobs the spring is required to have a high quality.( see __http://www.madehow.com/Volume-6/Springs.html)__ High quality does not always mean a stiff spring. What makes a spring stiff is a higher resisting force. The more a spring resist, the less it displaces. We can use this useful information in other inventions. For example when a vehicle has to go over large bumps it cause the parts to hit against with extreme force. By placing high resisting springs between these parts it makes the vehicle seem as if it never went over a bump. The reason the bump never effects the vehicles physical condition is because the spring pushes away on both parts with a high force. With the high resisting force it makes it seem as if the two parts were pushing away from each other. When the spring does this job it is said that the spring has absorbed shock. The heavier the vehicle means a heavier duty spring. In smaller cars there are lighter weight springs. Another reason springs are added to cars is for their handling. The way it helps handling out is it ensures that the bumps will not alter the movement of the tires. It helps with the alignment of the tires. Four springs with the same equilibrium will ensure the car stays even through it’s trip. Springs help the car stay off the tires. They help the car not rub against the tires also. (see __http://www.ehow.com/about_5675768_types-vehicle-coil-springs.html)__ Springs are also used for their stored energy. The reason this happens is because when a spring is displaced a mechanism that applies force holds it at this displacement. This held displacement is also called potential energy. It is referred to as potential energy because when the holding force is let off the spring will release and give off a force that we can calculate. An example of potential energy in a real life scenario is in a Nerf gun. A Nerf gun is a name of a dart gun company. In this gun you pull back on a piece that pulls the spring back. When you pull it back far enough the spring will lock behind a piece that holds it in place. When the spring locks, that is when you know that the energy you took to pull it back is stored. When you pull the trigger is pulled it releases the hold. When the hold is released the spring shoots forward. The reason it does this is because it is trying to reach its original state at the equilibrium. (see __http://zonalandeducation.com/mstm/physics/mechanics/energy/springPotentialEnergy/springPotentialEnergy.html__ and __http://zonalandeducation.com/mstm/physics/mechanics/energy/introduction/introduction.html)__ Without this equilibrium springs would be useless. The way we make use of the equilibrium is an incredible process. The process starts when the force is added. The more the force means there is more displacement. The displacement causes the spring to oscillate over the equilibrium point. If the spring is stiff it takes a lot more force to make the spring to oscillate over the equilibrium point. Depending on what problem scientist are trying to fix, they use different types of springs. The advances of what we have today come from using different forms of springs. The equilibrium is the most important state that a spring can be in. It determines where everything is supposed to stay at. Most things like to stay toward the equilibrium. Springs hold many objects at their equilibrium by using the springs original equilibrium. (see __http://books.google.com/books?id=aFNKqnC2E-sC&pg=PA286&lpg=PA286&dq=equilibrium+of+springs+examples&source=bl&ots=8LKlosaXE_&sig=iLELBL3aPnwNIivoiP4mbQiQtKM&hl=en&ei=tWGrTfaUG-nL0QHTx-n4CA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEsQ6AEwBw#v=onepage&q=equilibrium%20of%20springs%20examples&f=false__) In automobile crashes springs are one of the main reason that people survive. The reasoning behind this fact is that when a car is in crash the spring help slow down the force of the two crashing objects and increase the amount of impact time. The thicker the spring the more time it will take the two objects to collide. By increasing the amount of time in the impact we decrease the force of the impact. So in some case the thickness of the spring can really be effective. Some times when there is a crash that we can not figure out what caused it or how fast they were going, we can use the spring to determine many variables. How we can do this is by knowing the spring constant. After knowing this we can determine the displacement of the spring by observing penetrating objects. By using Hooke’s Law we plug it into the equation and we are resulted with impacting force. Many times when springs are altered from one another in a vehicle it will cause the balance of the car to be uneven. It may also affect the way the car drives. In many cases springs are designed to save lives at a disastrous point. (see __http://gafferongames.com/game-physics/spring-physics/__ ) Now for some work with Hooke’s law. The law stated again is F=kx. If there is a spring with a constant of 500N/m and it displaces 2 meters what would be the force? To calculate this we use the law. We can use the plug-n-chug method to determine the force. For x we have two meters and or k we have five hundred newtons per meter. As the equation states we must multiply these two numbers. The resulting number is one thousand. Now we must determine the units. We have newtons divided by meters times meters. The meters cancel each other out and we are left with newtons. This is a unit of force so we know we worked the equation correctly. Our final answer is one thousand newtons. Another problem is with the displacement and the force. We are trying to determine the spring constant for a given spring. We are given that the force of the spring is two hundred newtons when the spring is displaced at ten meters. Again we can use the plug-chug-method. We plug in two hundred newtons for force and ten meters for x, which is displacement. We see that the numbers are not on the same side of the equation so we have to divide the displacement on each side to get the equation equal to the constant. The equation should then be force over x is equal to k. In abbreviated form it would look like F/m=k. Now using the method we have two hundred over ten. The resulting number is twenty. Now for the units we have newtons over meters. ( see __http://www.mathkb.com/Uwe/Forum.aspx/algebra-help/252/Hooke-s-Law-problem)__ As stated earlier springs have a tendency to move in a simple harmonic motion. A spring will move over its equilibrium and back. It will repeat the simple harmonic motion until it reaches its equilibrium. Springs will tend to move in a straight path unless another force is acted upon it. With a mass and spring simulation we can see that the spring causes the mass to move in a straight path with simple harmonic motion. In the simple harmonic motion the weight is compressed and expanded over the equilibrium. These compressions and expansions are also forms of the displacement in Hooke’s Law. When the weight is compressed and expanded it tends to cross the equilibrium with same distance as each other. Once a spring is compressed it is harder to compress it farther than what it already is. The same is in the opposite direction which is expansion. The spring will move the weight perpendicular to what ever the opposite of the spring is connected to. The motion of the spring would remain constant if it where against a frictionless surface and there was no air resistance. With the simple harmonic motion we can predict the pattern of where the spring will be and when it will be there. These simple calculations are what Robert Hooke was trying to crack down on. He discovered most of his laws on these simple predictions. The motion of springs is quite the basic reason why they are useful to us other than their equilibrium point. Friction is a main factor that can either speed up slow down the acceleration of the spring. To find the acceleration of the spring we have to use some simple physic equations. We have force is equal to mass time acceleration. We also have Hooke’s Law of Force is equal to the spring constant times the displacement of the spring. Now that we have the two main equations we can use a substitution method. We replace the force for mass times acceleration with the spring constant times the displacement of the spring. Now the equation should look like ma=kx. Now we can divide each side by mass and we are equal to acceleration. The resulting equation should be acceleration is equal to the spring constant time the displacement of the spring over the mass. in variable form the equation should look like a=kx/m. ( see __http://www.studyphysics.ca/newnotes/20/unit03_mechanicalwaves/chp141516_waves/lesson42.htm__ and __http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm)__ Springs have a set wave pattern. With the spring’s simple harmonic motion we can figure a wave pattern over a graph. The reason behind the wave pattern is the oscillations. If we graph the expansions and compressions of the spring over a certain time period we will see a wave like pattern. In a frictionless and no air resistant environment the graphed wave will remain with the same amplitude every time. With the wave pattern we can view the period of the oscillation of the spring. The technology advancements have many back ground equations and examples. The wave shows us how the behavior of the spring can be used . If the oscillation of the spring stays the same then we have the period. With the period we can determine many uses for spring. (see __http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm)__ Every spring has a deforming point. Many things can affect this deforming point. Once you go beyond the deforming point it is near impossible to get the spring back to it original shape. Gravity is one of the main factors the can change the deforming point of a spring. The spring has to be in all correct calculations for it to work properly. If the spring has to much loaded force on it the spring will deform. The deformation of a spring can come in many forms. It can bend along one of it’s cylinder shape. It can unravel from its cylinder shape somewhere along the spring. The tighter the spring constant is then the more careful attention you have to pay attention to your other calculations. The reason we have to pay better attention is that if a little difference in the force capacity then the spring will deform greatly. The best way to find a spring’s deforming point is to actually test out your calculations. We can observe from these test how much load we can put on the similar type of spring. When the spring reacts to the pressure you know you are reaching the deforming point. Every spring has a limited amount of weight it can hold. The higher resistance a spring has then that means it has a higher deforming point. The thickness of the spring can affect the resisting force of the spring. So by putting these two together we can assume that the more thick a spring is then it will have a high deforming point on one area instead of over the whole spring like a skinny spring. Many people get confused and think thicker springs are more likely to deform, but in actuality skinny springs are more likely to deform due to their weak surface area. Thicker springs have a few weak points which if the right amount of force is applied then it will deform. Skinnier springs have these points all over which will spread out the deforming over these points. The best spring that is less likely to deform is one that is in between skinny and thick.( see __http://gafferongames.com/game-physics/spring-physics/__) The physics behind springs have evolved over many generations. The test and trial errors have accompanied in the advancements of springs. Robert Hooke also contributed a great deal to the technology behind springs. The many points that all make up springs help us today in our modern technology. From being made to being tested and being used is a long process. Many careful examinations are required to build a quality spring. There are many things that can affect the quality of springs. Knowing the background is quite fascinating.
There are many different types of springs. Most springs are made up of wire that has been wound multiple times into a circular shape. There are three basic types of wire springs. The first type of basic spring is the extension spring. The extension spring has tightly wound springs that are close together. When the spring is pulled on by an end and the other end is connected to something then it will pull back with the same amount of force to keep the object in it’s original place until the pull force exceeds the force it can pull back.
The next type of basic spring is the compression spring. This spring is wound to have spaces in between the wire. This spring is designed to shorten. The way this spring is shortened is that when a force is applied to an end it will push back with the same force. If there is to much force applied then the spring will deform and may bend.
The last type of basic spring is the torsion spring. This spring has two ends to it. there is just a few coils in between the two ends. When there is a force applied to both ends then the coils in the middle will tighten together. When the spring tightens it will pull it back to its original place. (see __http://school.mech.uwa.edu.au/~dwright/DANotes/springs/intro/intro.html__ also see __http://www.madehow.com/Volume-6/Springs.html__ )
Springs have been used through out history. Many things could have been used as spring type contraptions. The idea of a spring is to make the work easier of some task. The first type of springs that were used were non-coil type springs. A simple twig bending is an example of a type of spring force.
The way people back in b.c. have thought of ways to improve springs. They constructed ways out of metals and wood. Ctesibius of Alexandria came up with a procedure of making "springy bronze" by increasing the proportion of tin in the copper alloy, casting the part, and hardening it with hammer blows.(quotation from __http://www.madehow.com/Volume-6/Springs.html__ ) Many other B.C. figures also contributed to make springs better. The uses for springs are endless.
The main idea of a spring to do work is by how it can deform. After it deforms the spring should come back to its original shape and its position. Many other things were used in place of springs. For example clocks were controlled by a series of weights instead of a spring. The spring made the clock more accurate by being wound and back to its original position.
The way springs came into society was by someone doing an ordinary job. The job for example was necessary to survive. Hunting was one of the main ways to survive. people were inefficient at killing their prey. To improve their hunting strategies they invented a bow and arrow.
This spring like contraption probably kick started the need to learn more about how to improve this. It contributes to how we today got to such a complex design. There are many different types of designs. Different springs do different jobs. The basic design is to help how we live today. This is a major form of improved technology.
The technology behind springs is endless. There are so many things to account for. A few things are the deforming point, how much stress the spring can take, and the elasticity. A guy named Robert Hooke discovered a way to measure elasticity.
He called this Hooke’s law. In this law he described as an object deforms the force is greater. He also described the objects such as springs having a deforming limit beyond repair. He described this deformation as displacement of the molecules and ions in the material.
The deforming of the spring can happen through many ways. Some ways of the springs that they can deform are by stretching, pulling, squeezing, compressing, bending, or twisting the spring. The springs have the ideal form of elasticity according to Robert Hooke.
He stated that the F=kx or F=-kx, depending on the way you look at the constant. This basically states that when the force is applied then it is equal to the constant of the spring times the distance of deformation. He could calculate the spring constant by testing out springs. This helps us a lot today in our present times for simple task. Through just this simple equation we can find out how much load a spring can handle. The spring stores energy from when the force is applied.
The more force you apply the more the distance it displaces from the original shape. This means that the force applied is directly proportional to the distance it displaces. Once the force is taken away the spring goes back to its original position. Force can also be expressed in terms of stress. Stress can be applied through work.
(see __http://www.britannica.com/EBchecked/topic/271336/Hookes-law)__
Robert Hooke was a well known English scientist. He was born in Freshwater, Isle of Wight. He was almost as well known as Newton. Newton was one of his well known rival. He studied most of his life on how to make things better. He also discovered many things about microscopes.
Today his teachings and discoveries help us through a lot. The springs in vehicles help ride smooth. we can only imagine what life would be without springs.(see __http://www.rod.beavon.clara.net/robert_hooke.htm__ and __http://www.roberthooke.com/)__
Springs can also be thought as of waves. When the spring does the same repetitive motion from one end to the back it is said to be in a state of oscillation. The oscillation happens when there is a simple harmonic motion. The motion is going in a repetitive like motion. Springs are technically designed to do this motion. The motion helps many other inventions do what they were designed for. The equilibrium of the spring is what causes this. As Robert Hooke came to find this fact out he also used his knowledge to calculate the equilibrium constant. He viewed these springs as ether stretched or compressed. He saw that it would go almost that same distance in the opposite direction. When the constant increases the more force it requires to make the same distance of displacement. (see __http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section4.rhtml)__
Gravity may some times affects the way springs work. It applies a downward force on the spring. By knowing this we also know that there is always constant force in the downward direction on the spring. Springs are designed to resist this given force. The only time that gravity can be ignored is when the weight on the spring passes through its equilibrium with maximum speed. Because gravity sometimes affects springs, we can use springs to understand gravity better. (see __http://www.newton.dep.anl.gov/askasci/phy00/phy00636.htm)__
Using springs as pendulums we can view how gravity shifts. Because this shift we can observe how the Earth moves by just looking at the springs. For a little time the spring pendulum will go in a straight path but it will slowly shift. The oscillations are what most physicist look at. They also look at what direction its going in. The spring may also have a little bounce in it. These effects are because of how the Earth moves. (see __http://www.astro.oma.be/ICET/bim/bim138/vanruymbeke2.htm)__
The quality of a spring depends on how high quality of the steel is. There are other factors like how tightly the spring was wound that would differ the quality. Also the quality of the spring depends on the thickness of the wire. A spring that has a high tendency of reaching it’s equilibrium faster is said to be a high quality spring. Depending on the job the spring has to do determines where the equilibrium on the spring is. For more powerful jobs the spring is required to have a high quality.( see __http://www.madehow.com/Volume-6/Springs.html)__
High quality does not always mean a stiff spring. What makes a spring stiff is a higher resisting force. The more a spring resist, the less it displaces. We can use this useful information in other inventions. For example when a vehicle has to go over large bumps it cause the parts to hit against with extreme force. By placing high resisting springs between these parts it makes the vehicle seem as if it never went over a bump. The reason the bump never effects the vehicles physical condition is because the spring pushes away on both parts with a high force. With the high resisting force it makes it seem as if the two parts were pushing away from each other. When the spring does this job it is said that the spring has absorbed shock. The heavier the vehicle means a heavier duty spring. In smaller cars there are lighter weight springs. Another reason springs are added to cars is for their handling. The way it helps handling out is it ensures that the bumps will not alter the movement of the tires. It helps with the alignment of the tires. Four springs with the same equilibrium will ensure the car stays even through it’s trip. Springs help the car stay off the tires. They help the car not rub against the tires also. (see __http://www.ehow.com/about_5675768_types-vehicle-coil-springs.html)__
Springs are also used for their stored energy. The reason this happens is because when a spring is displaced a mechanism that applies force holds it at this displacement. This held displacement is also called potential energy. It is referred to as potential energy because when the holding force is let off the spring will release and give off a force that we can calculate. An example of potential energy in a real life scenario is in a Nerf gun. A Nerf gun is a name of a dart gun company. In this gun you pull back on a piece that pulls the spring back. When you pull it back far enough the spring will lock behind a piece that holds it in place. When the spring locks, that is when you know that the energy you took to pull it back is stored. When you pull the trigger is pulled it releases the hold. When the hold is released the spring shoots forward. The reason it does this is because it is trying to reach its original state at the equilibrium. (see __http://zonalandeducation.com/mstm/physics/mechanics/energy/springPotentialEnergy/springPotentialEnergy.html__ and __http://zonalandeducation.com/mstm/physics/mechanics/energy/introduction/introduction.html)__
Without this equilibrium springs would be useless. The way we make use of the equilibrium is an incredible process. The process starts when the force is added. The more the force means there is more displacement. The displacement causes the spring to oscillate over the equilibrium point. If the spring is stiff it takes a lot more force to make the spring to oscillate over the equilibrium point. Depending on what problem scientist are trying to fix, they use different types of springs. The advances of what we have today come from using different forms of springs. The equilibrium is the most important state that a spring can be in. It determines where everything is supposed to stay at. Most things like to stay toward the equilibrium. Springs hold many objects at their equilibrium by using the springs original equilibrium. (see __http://books.google.com/books?id=aFNKqnC2E-sC&pg=PA286&lpg=PA286&dq=equilibrium+of+springs+examples&source=bl&ots=8LKlosaXE_&sig=iLELBL3aPnwNIivoiP4mbQiQtKM&hl=en&ei=tWGrTfaUG-nL0QHTx-n4CA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEsQ6AEwBw#v=onepage&q=equilibrium%20of%20springs%20examples&f=false__)
In automobile crashes springs are one of the main reason that people survive. The reasoning behind this fact is that when a car is in crash the spring help slow down the force of the two crashing objects and increase the amount of impact time. The thicker the spring the more time it will take the two objects to collide. By increasing the amount of time in the impact we decrease the force of the impact. So in some case the thickness of the spring can really be effective. Some times when there is a crash that we can not figure out what caused it or how fast they were going, we can use the spring to determine many variables. How we can do this is by knowing the spring constant. After knowing this we can determine the displacement of the spring by observing penetrating objects. By using Hooke’s Law we plug it into the equation and we are resulted with impacting force. Many times when springs are altered from one another in a vehicle it will cause the balance of the car to be uneven. It may also affect the way the car drives. In many cases springs are designed to save lives at a disastrous point. (see __http://gafferongames.com/game-physics/spring-physics/__ )
Now for some work with Hooke’s law. The law stated again is F=kx. If there is a spring with a constant of 500N/m and it displaces 2 meters what would be the force? To calculate this we use the law. We can use the plug-n-chug method to determine the force. For x we have two meters and or k we have five hundred newtons per meter. As the equation states we must multiply these two numbers. The resulting number is one thousand. Now we must determine the units. We have newtons divided by meters times meters. The meters cancel each other out and we are left with newtons. This is a unit of force so we know we worked the equation correctly. Our final answer is one thousand newtons.
Another problem is with the displacement and the force. We are trying to determine the spring constant for a given spring. We are given that the force of the spring is two hundred newtons when the spring is displaced at ten meters. Again we can use the plug-chug-method. We plug in two hundred newtons for force and ten meters for x, which is displacement. We see that the numbers are not on the same side of the equation so we have to divide the displacement on each side to get the equation equal to the constant. The equation should then be force over x is equal to k. In abbreviated form it would look like F/m=k. Now using the method we have two hundred over ten. The resulting number is twenty. Now for the units we have newtons over meters. ( see __http://www.mathkb.com/Uwe/Forum.aspx/algebra-help/252/Hooke-s-Law-problem)__
As stated earlier springs have a tendency to move in a simple harmonic motion. A spring will move over its equilibrium and back. It will repeat the simple harmonic motion until it reaches its equilibrium. Springs will tend to move in a straight path unless another force is acted upon it. With a mass and spring simulation we can see that the spring causes the mass to move in a straight path with simple harmonic motion. In the simple harmonic motion the weight is compressed and expanded over the equilibrium. These compressions and expansions are also forms of the displacement in Hooke’s Law. When the weight is compressed and expanded it tends to cross the equilibrium with same distance as each other. Once a spring is compressed it is harder to compress it farther than what it already is.
The same is in the opposite direction which is expansion. The spring will move the weight perpendicular to what ever the opposite of the spring is connected to. The motion of the spring would remain constant if it where against a frictionless surface and there was no air resistance. With the simple harmonic motion we can predict the pattern of where the spring will be and when it will be there. These simple calculations are what Robert Hooke was trying to crack down on. He discovered most of his laws on these simple predictions. The motion of springs is quite the basic reason why they are useful to us other than their equilibrium point. Friction is a main factor that can either speed up slow down the acceleration of the spring. To find the acceleration of the spring we have to use some simple physic equations. We have force is equal to mass time acceleration. We also have Hooke’s Law of Force is equal to the spring constant times the displacement of the spring. Now that we have the two main equations we can use a substitution method. We replace the force for mass times acceleration with the spring constant times the displacement of the spring. Now the equation should look like ma=kx. Now we can divide each side by mass and we are equal to acceleration. The resulting equation should be acceleration is equal to the spring constant time the displacement of the spring over the mass. in variable form the equation should look like a=kx/m. ( see __http://www.studyphysics.ca/newnotes/20/unit03_mechanicalwaves/chp141516_waves/lesson42.htm__ and __http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm)__
Springs have a set wave pattern. With the spring’s simple harmonic motion we can figure a wave pattern over a graph. The reason behind the wave pattern is the oscillations. If we graph the expansions and compressions of the spring over a certain time period we will see a wave like pattern. In a frictionless and no air resistant environment the graphed wave will remain with the same amplitude every time. With the wave pattern we can view the period of the oscillation of the spring. The technology advancements have many back ground equations and examples. The wave shows us how the behavior of the spring can be used . If the oscillation of the spring stays the same then we have the period. With the period we can determine many uses for spring. (see __http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm)__
Every spring has a deforming point. Many things can affect this deforming point. Once you go beyond the deforming point it is near impossible to get the spring back to it original shape. Gravity is one of the main factors the can change the deforming point of a spring. The spring has to be in all correct calculations for it to work properly. If the spring has to much loaded force on it the spring will deform. The deformation of a spring can come in many forms. It can bend along one of it’s cylinder shape. It can unravel from its cylinder shape somewhere along the spring. The tighter the spring constant is then the more careful attention you have to pay attention to your other calculations. The reason we have to pay better attention is that if a little difference in the force capacity then the spring will deform greatly. The best way to find a spring’s deforming point is to actually test out your calculations. We can observe from these test how much load we can put on the similar type of spring. When the spring reacts to the pressure you know you are reaching the deforming point. Every spring has a limited amount of weight it can hold. The higher resistance a spring has then that means it has a higher deforming point. The thickness of the spring can affect the resisting force of the spring. So by putting these two together we can assume that the more thick a spring is then it will have a high deforming point on one area instead of over the whole spring like a skinny spring. Many people get confused and think thicker springs are more likely to deform, but in actuality skinny springs are more likely to deform due to their weak surface area. Thicker springs have a few weak points which if the right amount of force is applied then it will deform. Skinnier springs have these points all over which will spread out the deforming over these points. The best spring that is less likely to deform is one that is in between skinny and thick.( see __http://gafferongames.com/game-physics/spring-physics/__)
The physics behind springs have evolved over many generations. The test and trial errors have accompanied in the advancements of springs. Robert Hooke also contributed a great deal to the technology behind springs. The many points that all make up springs help us today in our modern technology. From being made to being tested and being used is a long process. Many careful examinations are required to build a quality spring. There are many things that can affect the quality of springs. Knowing the background is quite fascinating.